Um estudo histórico-epistemológico e matemático do Tratado Aritmético de al-Khwarizm

Abstract

This work is a historical, epistemological and mathematical study of the work of alKhwarizm, written in the early 9th century in Baghdad. The work discusses the positional decimal system used by the Indians. Its content begins by presenting the numerals and their writing rules to form numbers and continues by showing the algorithms of arithmetic operations; in short, it is a manual for those who want to learn Indian arithmetic. Throughout our study, we refer to the work as the Arithmetic Treatise of al-Khwarizm. There is no record of the original Arabic text and the work has been preserved only in a Latin manuscript, dated from the 14th century, preserved and catalogued in the Cambridge University Library, under number I.i.6.5. The Cambridge manuscript was translated into Russian by A. P. Yushkiévitch and, from the Russian translation by Yushkiévitch (1983), we made a translation into Portuguese, in order to be used in our study. Adopting a historiographical perspective that contextualizes past knowledge in its time and space of elaboration, we analyzed the Arithmetic Treatise of al-Khwarizm with a focus on the numbers and algorithms used by the author in the work. To this end, we conducted a detailed bibliographical-documentary study consisting of reading, translating, and understanding the procedures of the main document, the Arithmetic Treatise of al-Khwarizm, and from this, we listed the contextual elements of the work that needed to be further studied. We conducted a historical, epistemological, and mathematical study of the Treatise and concluded that, although the decimal and positional numeration system presented by al-Khwarizm has characteristics in common with the modern numeration system, the calculation algorithms differ due to the material conditions and knowledge available at the time in the Near East.